measure_features: Measures of network topological features

In manynet: Many Ways to Make, Modify, Map, Mark, and Measure Myriad Networks

Measures of network topological features

Description

These functions measure certain topological features of networks:

• net_core() measures the correlation between a network and a core-periphery model with the same dimensions.

• net_richclub() measures the rich-club coefficient of a network.

• net_factions() measures the correlation between a network and a component model with the same dimensions. If no 'membership' vector is given for the data, node_partition() is used to partition nodes into two groups.

• net_modularity() measures the modularity of a network based on nodes' membership in defined clusters.

• net_smallworld() measures the small-world coefficient for one- or two-mode networks. Small-world networks can be highly clustered and yet have short path lengths.

• net_scalefree() measures the exponent of a fitted power-law distribution. An exponent between 2 and 3 usually indicates a power-law distribution.

• net_balance() measures the structural balance index on the proportion of balanced triangles, ranging between 0 if all triangles are imbalanced and 1 if all triangles are balanced.

These ⁠net_*()⁠ functions return a single numeric scalar or value.

Usage

net_core(.data, mark = NULL)

net_richclub(.data)

net_factions(.data, membership = NULL)

net_modularity(.data, membership = NULL, resolution = 1)

net_smallworld(.data, method = c("omega", "sigma", "SWI"), times = 100)

net_scalefree(.data)

net_balance(.data)

Arguments

.data	An object of a manynet-consistent class: matrix (adjacency or incidence) from {base} R edgelist, a data frame from {base} R or tibble from {tibble} igraph, from the {igraph} package network, from the {network} package tbl_graph, from the {tidygraph} package
mark	A logical vector the length of the nodes in the network. This can be created by, among other things, any ⁠node_is_*()⁠ function.
membership	A vector of partition membership.
resolution	A proportion indicating the resolution scale. By default 1, which returns the original definition of modularity. The higher this parameter, the more smaller communities will be privileged. The lower this parameter, the fewer larger communities are likely to be found.
method	There are three small-world measures implemented: "sigma" is the original equation from Watts and Strogatz (1998), \frac{\frac{C}{C_r}}{\frac{L}{L_r}} , where C and L are the observed clustering coefficient and path length, respectively, and C_r and L_r are the averages obtained from random networks of the same dimensions and density. A \sigma > 1 is considered to be small-world, but this measure is highly sensitive to network size. "omega" (the default) is an update from Telesford et al. (2011), \frac{L_r}{L} - \frac{C}{C_l} , where C_l is the clustering coefficient for a lattice graph with the same dimensions. \omega ranges between 0 and 1, where 1 is as close to a small-world as possible. "SWI" is an alternative proposed by Neal (2017), \frac{L - L_l}{L_r - L_l} \times \frac{C - C_r}{C_l - C_r} , where L_l is the average path length for a lattice graph with the same dimensions. SWI also ranges between 0 and 1 with the same interpretation, but where there may not be a network for which SWI = 1.
times	Integer of number of simulations.

Modularity

Modularity measures the difference between the number of ties within each community from the number of ties expected within each community in a random graph with the same degrees, and ranges between -1 and +1. Modularity scores of +1 mean that ties only appear within communities, while -1 would mean that ties only appear between communities. A score of 0 would mean that ties are half within and half between communities, as one would expect in a random graph.

Modularity faces a difficult problem known as the resolution limit (Fortunato and Barthélemy 2007). This problem appears when optimising modularity, particularly with large networks or depending on the degree of interconnectedness, can miss small clusters that 'hide' inside larger clusters. In the extreme case, this can be where they are only connected to the rest of the network through a single tie. To help manage this problem, a resolution parameter is added. Please see the argument definition for more details.

Source

{signnet} by David Schoch

References

On core-periphery

Borgatti, Stephen P., and Martin G. Everett. 2000. “Models of Core/Periphery Structures.” Social Networks 21(4):375–95. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1016/S0378-8733(99)00019-2")}

On the rich-club coefficient

Zhou, Shi, and Raul J. Mondragon. 2004. "The Rich-Club Phenomenon in the Internet Topology". IEEE Communications Letters, 8(3): 180-182. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1109/lcomm.2004.823426")}

On modularity

Newman, Mark E.J. 2006. "Modularity and community structure in networks", Proceedings of the National Academy of Sciences 103(23): 8577-8696. \Sexpr[results=rd]{tools:::Rd_expr_doi("https://doi.org/10.1073/pnas.0601602103")}

Murata, Tsuyoshi. 2010. "Modularity for Bipartite Networks". In: Memon, N., Xu, J., Hicks, D., Chen, H. (eds) Data Mining for Social Network Data. Annals of Information Systems, Vol 12. Springer, Boston, MA. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1007/978-1-4419-6287-4_7")}

On small-worldliness

Watts, Duncan J., and Steven H. Strogatz. 1998. “Collective Dynamics of ‘Small-World’ Networks”. Nature 393(6684):440–42. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/30918")}

Telesford QK, Joyce KE, Hayasaka S, Burdette JH, Laurienti PJ. 2011. "The ubiquity of small-world networks". Brain Connectivity 1(5): 367–75. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1089/brain.2011.0038")}

Neal, Zachary P. 2017. "How small is it? Comparing indices of small worldliness". Network Science. 5 (1): 30–44. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1017/nws.2017.5")}

On scale-free networks

Barabasi, Albert-Laszlo, and Reka Albert. 1999. "Emergence of scaling in random networks", Science, 286(5439): 509-512. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1126/science.286.5439.509")}

Clauset, Aaron, Cosma Rohilla Shalizi, and Mark E.J. Newman. 2009. "Power-law distributions in empirical data", SIAM Review, 51(4): 661-703. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1137/070710111")}

Stumpf, Michael P.H., and Mason Porter. 2012. "Critical truths about power laws", Science, 335(6069): 665-666. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1126/science.1216142")}

Holme, Petter. 2019. "Rare and everywhere: Perspectives on scale-free networks", Nature Communications, 10(1): 1016. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1038/s41467-019-09038-8")}

On balance theory

Heider, Fritz. 1946. "Attitudes and cognitive organization". The Journal of Psychology, 21: 107-112. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1080/00223980.1946.9917275")}

Cartwright, D., and Frank Harary. 1956. "Structural balance: A generalization of Heider's theory". Psychological Review, 63(5): 277-293. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1037/h0046049")}

See Also

net_transitivity() and net_equivalency() for how clustering is calculated

Other measures: measure_attributes, measure_central_between, measure_central_close, measure_central_degree, measure_central_eigen, measure_closure, measure_cohesion, measure_diffusion_infection, measure_diffusion_net, measure_diffusion_node, measure_heterogeneity, measure_hierarchy, measure_holes, measure_periods, measure_properties, member_diffusion

Examples

net_core(ison_adolescents)
net_core(ison_southern_women)
net_richclub(ison_adolescents)
  net_factions(ison_southern_women)
net_modularity(ison_adolescents, 
  node_in_partition(ison_adolescents))
net_modularity(ison_southern_women, 
  node_in_partition(ison_southern_women))
net_smallworld(ison_brandes)
net_smallworld(ison_southern_women)
net_scalefree(ison_adolescents)
net_scalefree(generate_scalefree(50, 1.5))
net_scalefree(create_lattice(100))
net_balance(ison_marvel_relationships)

manynet documentation built on June 23, 2025, 9:07 a.m.